A model planet showing coupling between life and its environment

1. NANIA2D - Daisyworld Graeme Ackland (physicist)Tim Lenton (ecologist)Michael Clark (project student) School of Physics, University of Edinburgh A model planet showing coupling between life and its environment Journal of Theoretical Biology 223 39 (2003) Journal of Theoretical Biology 227 121 (2004)

2. Gaia Theory: the world is a strongly interacting system William Golding – Nobel laureate Oxford physics undergraduate James Lovelock – inventor of electron capture detector And 0D daisyworld

3. What would count as life? • Define life as an open thermodynamic system which stays away from equilibrium. • Life is a property of the planet as a whole – detectable homeostasis of temperature, salinity, chemical equilibrium in the atmosphere • LOVELOCK: following this definition No: the atmosphere is in equilibrium. • Is there a better definition? (That excludes cars) • That Darwin would have understood?

4. CONFLICT • Neo-darwinism – every gene for itself • Gaia theory – Life modifies its environment to be favourable for life. RESOLUTION Self organisation

5. Evolution TEMPERATURE: diffusion equation Stefan Radiation Heat Capacity Absorption Diffusion Rate Toy java applet version of daisyworld available at: http://www.ph.ed.ac.uk/nania/daisyworld/daisyworld.html

6. Stochastic daisy evolution rules Death Growth γ constant b : Quadratic in T b= (T-Tc)2 +1

7. Spread of albedo with insolation

8. Biodiversity as entropy • Define entropy by spread of albedo Maximum entropy implies This is not the biologists definition of biodiversity (except sometimes it is)

9. Albedo self-organises • Temperature self regulates at optimum for daisy growth, globally and locally. • Many albedo distributions are consistent with temperature self-regulation. • Albedo maximises entropy for case of infinite thermal conductivity Max[ p(A) ln p(A) ] subject to mean <A>=A(S) and 0<A<1… NA = N0 exp(-bA) • Finite conduction leads to peak in albedo at self-optimising value. Local structure.

10. MaxEnt not observed for finite conductivity Moves with Increased S Flattens with Increased D

11. Some Maths ! Maximisation Principle? • Growth: optimised at Tg • Death: optimised at Td How will system self-organise? 1/ Maximise entropy production … T=Td 2/ Maximise “living” sites …T=Tg

12. A general principle of replicator dynamics? 2D daisyworld Logistic Map

13. Maximum life principle? • Two species: daisies and trees. • Do not compete directly (for space) • Compete indirectly (different preferred T) Where NT+ND>1 coexistence, uniform T; Where NT+ND<1 separation, binary T; Feedback between T and A prevents invasion. bT= 1-(T-TT)2bD =1- (T-TD)2

14. Response time of daisyworld Heat absorbed (black) emitted (red) as insolation is suddenly increased every 200 mean lifetimes.

15. A new adaptive genetic algorithm • Growth function b = F(T1…TN,t) • Variables = multiple “temperatures”; time • Average temperature(s) maximises b • Diverse set of albedos remain. System can adapt if growth function changes in time. • Work in progress.

16. Why are ecosystems complex? • Traditional models of ecosystems give complex population dynamics (right) • Simple food webs of predator-prey interactions (wrong) • What’s missing? … evolution & feedback • Ackland and Gallagher, Phys.Rev.Letters 93, 158701 (2004)

17. ECOSystem Simulation Environment • Generalised Lotka-Volterra equations: • For autotrophs, with x0 limiting the population • dxi/dt = xi – xi2/x0 + SjMij xi xj. • For heterotrophs – food limited • dxi/dt = SjMij xi xj - c xi • (NEW) Link strengths change – strategy or evolution • dMij/dt = e (Ni-Nj)Mij • Toy applet version available at: http://www.ph.ed.ac.uk/nania/ecosse/ecosse.html

18. Chaotic Population dynamics Increased use of resources Population Flow in=sum of positive terms

19. Scale-free interactions Emergent from evolving model Predators have multiple prey All different levels of importance Changing in time Consequences Stable, multiply connected food web. No loops: A eats B, B eats C, C eats A